1. Field of the Invention
The present invention relates to an acoustic reflector (acoustic mirror) for a BAW resonator (BAW=bulk acoustic wave), and here in particular to an acoustic reflector with a plurality of layers for an improved performance of the BAW resonator.
2. Description of the Related Art
The present invention preferably involves BAW filters for RF applications, and here in particular BAW filters for RF applications in which excellent selectivity and steep transition bands are required. In such filters, the most critical parameters are the quality factor and the coupling coefficient of the BAW resonators. The coupling coefficient is defined by the frequencies at which series resonance and parallel resonance occur. The coupling coefficient is a function of the electromechancial coupling of the piezoelectric layer of the BAW resonator as well as the thickness and types of materials uses in the overall arrangement of the BAW resonator having a plurality of layers to form a layer stack. With respect to the above-mentioned series resonance and parallel resonance, it should be understood that hereby the electrical resonance performance of a BAW resonator is to be understood, i.e. a series resonance corresponds to the impedance minimum and the parallel resonance to the impedance maximum of the frequency-dependent characteristic impedance curve of the resonator.
The quality is defined by the relative energy loss in the BAW resonator. The energy loss is either based on the leaking of acoustic signals, which is also referred to as acoustic leakage, electrical effects, or viscous losses (damping) of the acoustic waves in the layer stack.
FIG. 1A shows a schematic illustration of a conventional BAW resonator having a resonance frequency of about 1840 MHz in the embodiment shown. The BAW resonator 100 includes a piezoelectric layer 102, such as from aluminum nitride (AlN). Furthermore, the BAW resonator 100 includes a top electrode 104 that may itself be constructed from several metallic and dielectric layers. The bottom electrode 106 of the BAW resonator 100 may also be constructed from several metallic and dielectric layers.
In the example shown, the bottom electrode 106 includes a first layer 106a from a material with low impedance, e.g. aluminum (Al), and a second layer 106b from a material with high acoustic impedance, e.g. tungsten (W).
In the example illustrated, the piezoelectric layer 102 has a thickness of 1200 nm. As mentioned, the top electrode 104 may include a plurality of layers, an Al layer of the top electrode 104 having a thickness of about 200 nm, and a W layer of the top electrode 104 having a thickness of about 150 nm. The W layer 106a of the bottom electrode 106 has a thickness of about 150 nm, and the Al layer 106b of the bottom electrodes 106 has a thickness of about 200 nm.
The BAW resonator according to FIG. 1A further includes a substrate 108, such as a silicon substrate. On a surface of the substrate, facing the resonator element 100, an acoustic mirror or acoustic reflector 110 is formed, which is disposed between the substrate 108 and the bottom electrode 106. The acoustic mirror 110 includes a plurality of layers 112, 114, 116, 118, 120 made from a material with high acoustic impedance and a material with low acoustic impedance, with layers from a material with high acoustic impedance and layers from a material with low acoustic impedance being alternately disposed. The mirror 110 is designed for the above-mentioned resonance frequency of about 1840 MHz of the resonator. Here, a λ/4 mirror is involved, as it is conventionally used.
The first layer 112 consists of a material with low acoustic impedance, e.g. SiO2, the second layer 114 consists of a material with high acoustic impedance, e.g. W, the third layer 116 consists of a material with low acoustic impedance, e.g. SiO2, the fourth layer 118 consists of a material with high acoustic impedance, e.g. W, and the fifth layer 120 consists of a material with low acoustic impedance, e.g. SiO2. In the example illustrated, the layers 112, 116, and 120 are SiO2 layers of equal thickness, e.g. 810 nm at the considered resonance frequency, and the layers 114 and 118 are W layers of equal thickness, e.g. 710 nm at the considered resonance frequency.
The typical Q-factor, as it can be obtained for a BAW resonator on an acoustic mirror, as it is exemplarily shown in FIG. 1A, ranges from about 400 to 700. Although these values are sufficient to keep pace with SAW devices (SAW=surface acoustic wave) for applications in the mobile phone area, these values are barely sufficient enough to produce, for example, antenna duplexers or other demanding low-loss/high-selectivity filters, e.g. US-CDMA filters or W-CDMA filters. Duplexers available on the market today are large ceramic components because the SAW filters do not have sufficient power handling capability. CDMA filters are often made by so-called “split-band” SAW filters using two filters connected in parallel with different center frequencies, because a single SAW filter would not have sufficiently steep transition characteristics.
It should be mentioned here that an improvement of the quality for BAW resonators to values greater than 700 is not only of great interest for CDMA filters. In general, an improvement in the quality of the resonators leads to a performance improvement of the filters (e.g. filter band width increase and/or improvement of the standing wave ratio) and thus to a better yield in the mass production of these devices.
For the above-mentioned loss mechanisms, no widely accepted theory exists with respect to that mechanism that is dominant in BAW resonators. Viscous losses (material damping) and electrical losses by the ohmic resistance of the electrodes and the wiring have so far been regarded as main suspects. Electrical losses have been well characterized and it can be shown that these are not the dominating losses. Viscous losses are unlikely to represent a limiting factor, because secondary acoustic modes in the resonators very often have very high Q-factors that would not be present if the materials themselves would cause a strong damping of the acoustic waves. Thus, experimental results of overmode resonators with qualities of 68000 have been shown, for example, by K. M. Lakin et al., IEEE Trans. Microwave Theory, Vol. 41, No. 12, 1993.
Interferometric measurements have shown that part of the energy is also lost by lateral acoustic waves, which means that the energy trapping does not work perfectly. In order to avoid this loss mechanism, an experimental resonator with an “air” trench (unfilled trench) surrounding the active area has been constructed so that no waves could escape in the lateral direction. This experimental arrangement led to the surprising result that the Q-factor changed only marginally as opposed to conventional resonator elements, which is an indication that the energy loss by lateral acoustic waves is also not dominating.
It has already been possible to experimentally show that a rough substrate backside (wafer backside) has a significant influence on the secondary modes in BAW resonators having acoustic mirrors. This is to be seen as indication that vertical waves are to be considered as possible sources of losses, In order to verify this, samples having polished backsides have been prepared. It has been found that strong reflections of the waves from the backside occurred after polishing, which were not present in the samples with the rough backside. This means that, in the sample with the polished backsides, the acoustic wave energy that has before been scattered and consequently lost at the rough backside surface is now reflected back and fed back into the piezoelectric layer. Furthermore, using laser interferometry, the inventors could prove that vibrations are present at the backside. Since the acoustic mirrors for the longitudinal waves in the resonator element at its operation frequency are optimized, it is a strong indication that the waves observed at the backside are shear waves.
At this point, it should be noted that all relevant publications on acoustic mirrors for BAW resonators only describe the reflectivity of the mirror for longitudinal waves, i.e. waves propagating in the direction of the elastic deflection, because this is the only obvious wave type generated by conventional strongly oriented piezoelectric thin film layers. Furthermore, this wave type is that defining the main resonance of a BAW element by a standing wave condition in the stack. Acoustic mirrors are Bragg reflectors having various layers with high and low acoustic impedance. Conventionally, layer thicknesses are used, which lie as close as possible to a dimension in the area of λ/4 (λ=wavelength) of the longitudinal waves, because here an optimum reflectivity at the main resonance frequency is achieved.
Shear waves are not excited in ideal, infinitely large resonators, because there is no piezoelectrical coupling between a vertical electrical field and the shear stresses in a piezo layer with a dominant C-axis crystal orientation. In the prior art, no publication is known, which explains or describes the effect of shear waves in thin layer BAW resonators. There are three reasons why shear waves are yet generated in real resonators:
(a) In the piezoelectric layer of the BAW resonator, tilted grain boundaries may occur. If this tilt has even a small portion of a preferred direction, then a vertical field may lead to launch of shear waves in the piezoelectric layer.
(b) At the edges of a resonator, certain acoustic edge conditions for boundary area between the active area and the outside area must be fulfilled. If these boundary conditions between the outside area and the active area are not well adapted to each other, a generation of shear waves at the circumference of the resonator may occur. In physical terms, the lateral boundary wall of the resonator leads to the generation of acoustic scattering waves propagating in all spatial directions (of course only within the solid) and with all possible polarizations, which is illustrated schematically in FIG. 1B. In FIG. 1B, the resonator is schematically shown at 200, which includes the electrodes 104 and 106 shown in FIG. 1A as well as the piezoelectric layer 102. The mirror is schematically shown at 202. The arrow 204 illustrates the longitudinal excitation in the entire active area of the device. The arrows 206 and 208 show scattering waves occurring at the edge of the resonator 200, the scattering waves including both longitudinal portions 210 (straight arrows) and shear wave portions 212 (wavy arrows).
(c) The longitudinal waves 210 moving in a direction not exactly perpendicular to the substrate plans (see FIG. 1B) are at least partly converted to shear waves 212 at the interfaces 213 of the different layers. The shear waves 212 may then easily pass the acoustic mirror 202, because it is only optimized for a reflection of the longitudinal waves.
Since most film materials for acoustic resonators have Poisson ratios ranging from about 0.17 to 0.35, the velocity of the shear waves is usually at about half of the velocity of the longitudinal waves. For this reason, with λ/4 mirrors designed for the reflection of longitudinal waves, it may easily occur that the shear waves are not reflected well enough. In fact, the acoustic layer thickness of the layers of the mirror lies at about λ/2 for shear waves, which exactly corresponds to the anti-reflection condition for this type of wave (i.e. a transmission as high as possible).
This situation is explained in greater detail in FIG. 1C for the example shown in FIG. 1A of a BAW resonator with the dimensions indicated there. Across a frequency area from 1 GHz to 4 GHz, the transmittance of the acoustic mirror 110 there illustrated for longitudinal waves 210 existing in the BAW resonator and shear waves 212. At this point, it should be understood that all layers below the piezoelectric layer 102, i.e. in the example shown in FIG. 1A, the layers 106a, 106b, 112, 114, 116, 118, and 120, are to be taken into account in their effect as acoustic reflector, i.e. in particular also the layers 106a and 106b of the bottom electrode 106. The reason for this is that the electrodes also have a reflecting effect on the acoustic waves generated in the piezoelectric layer. The property of “reflectivity” can only be associated with the entirety of all layers lying beneath the piezoelectric layer 102 in a meaningful manner, so that by the term “acoustic reflector” or “acoustic mirror”, in considering the reflection property thereof, the entirety of the layers is to be understood, which are disposed between the piezoelectric layer 102 and the substrate 108.
In order to calculate the reflectivity of an acoustic mirror with n layers (in FIG. 1A n=5 Bragg layers+2 electrode layers=7), the transformation equation of a terminating resistor through a long line (see equation (1) below) may be used, which is obtained from the so-called Mason model (see W. P. Mason, Physical Acoustics I, Part A, Academic Press, NY, 1994), to obtain an overall impedance Zi (see K. M. Lakin et al, IEEE Trans. Microwave Theory, Vol. 41, No. 12, 1993). The following applies:                               Z          i                =                              z            i                    ⁡                      [                                                                                                      Z                                              i                        -                        1                                                              ·                    cos                                    ⁢                                                                           ⁢                                      Θ                    i                                                  +                                                      i                    ·                                          z                      i                                        ·                    sin                                    ⁢                                                                           ⁢                                      Θ                    i                                                                                                                                          z                      i                                        ·                    cos                                    ⁢                                                                           ⁢                                      Θ                    i                                                  +                                                      i                    ·                                          Z                                              i                        -                        1                                                              ·                    sin                                    ⁢                                                                           ⁢                                      Θ                    i                                                                        ]                                              (        1        )            with:                i=1. . . n, wherein “1” numbers the layer adjacent to the substrate, and “n” the layer adjacent to the piezo layer,        zi=the acoustic impedance of the considered layer i,        Zi−1=the entire acoustic impedance of the so-far considered layers 1 to i−1, and        θi=the entire phase across the layer i.        θi is determined according to the following calculation rule:                               Θ          i                =                              ω            ·                          d              i                                            v            i                                              (        2        )            with:        vi=the velocity of the acoustic wave in the layer i, depending on the polarization state.        di=the thickness of the layer i and,        ω=angular frequency.        
For a given stack, see e.g. FIG. 1A, it is being started with the calculation of the entire input impedance to the first layer 112 adjacent to the substrate 108 using the above equations, wherein for the first calculation Zi−1=Zsub=substrate impedance and zi=z1=acoustic impedance of layer 1 (layer 112 in FIG. 1A) applies. For the next layer, layer 2 (layer 114 in FIG. 1A), the above equations are also used, wherein then Zi−1=Z1=calculated entire impedance up to the layer 1, and the other parameters as for layer 2 apply. This calculation is repeated for all layers up to the piezoelectric layer.
The mirror reflection coefficient is then calculated according to the following calculation rule:                     R        =                                            Z              n                        -                          z              p                                                          Z              n                        +                          z              p                                                          (        3        )            with:                Zn=calculated impedance of all mirror and electrode layers, and        Zp=the acoustic impedance of the piezoelectric layer.        
In general, the reflection coefficient is a complex value whose magnitude describes the amplitude of the reflected wave (related to the amplitude of the incident wave), and whose phase mirrors the effective phase jump of the reflected wave.
The above calculation may be calculated both for longitudinal waves and shear waves using the values exemplarily indicated in the following table for different materials for acoustic impedances and wave velocities for the different waves.
vi for azi for azs for alongitudinallongitudinalVs for ashear waveMaterialwavewave (106 kg/m2s)shear wave(106 kg/m2s)Al 6422 m/s17.33110 m/s8.4W 5230 m/s1012860 m/s55.2AlN10400 m/s346036 m/s19.7SiO2 5970 m/s13.13760 m/s8.3Si 8847 m/s19.35300 m/s11.6SiN11150 m/s36.2616020
Based on the above values, the reflectivity of the mirror may be calculated both for longitudinal waves and shear waves. If the result is to be expressed as transmissivity in dB, it is calculated as follows:TdB=10·log(1−|R|2).
As can be seen from FIG. 1C, the curve of the transmittance of the mirror is very low for longitudinal waves 210 in the area of the operation frequency of about 1.8 GHz (at about −38 dB), i.e. longitudinal waves are very strongly reflected in the frequency range of about 1.0 to 2.7 GHz, i.e. the mirror has high reflectivity. Considering the transmittance of the mirror for the shear waves 212, shown in comparison therewith, it can easily be recognized that here the transmissivity in the area of the operation frequency (1.8 GHz) is very high (about −2 dB) for the shear waves, i.e. a large portion of the energy transported by the shear waves is not reflected, but leaks from the BAW resonator and is lost.